IK on legs works only after you rotate a bone in the IK chain
First of all, if you don't want to add a pole bone (and I didn't understand why) in edit mode you can slightly move forward (Y axis) the knee bone: in this way the IK solver will try the front movement as first solution.

In a IK chain, limits should be set in the properties panel, bones, Inverse Kinematics tab, instead of bones constraints (this has to be done for every bone of the chain).

In your file all thoose values are wrong: I don't know which kind of constraint you need but I suggest you to remove all constraint and readd them one by one (the red line shows the allowed movement of every bone).